Title

Author

Date of Submission

Spring 2017

Academic Programs and Concentrations

Mathematics

Project Advisor 1

Steven Simon

Abstract/Artist's Statement

Can any three blobs in \rr^3 be bisected by a single plane, so that half of each blob is on either side of the plane? The answer is yes, and with project adviser, Steven Simon, I will be researching mass equipartition problems like this one in more dimensions with more blobs and more (hyper)planes. This problem involves first looking at the symmetries of these hyperplanes, from which the group \zz_2^k arises. We next look at the group of homomorphisms H^1(\zz_2^k) from \zz_2^k to the unit hypersphere in order to better understand \zz_2^k. Using this group of homomorphisms as a basis, the coefficients of these homomorphisms uniquely determine a partition of the blobs. I will get the chance to examine where these coefficients are zero, corresponding to an equipartition of the blobs, by doing computations inside polynomial rings.